Problem: A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$7.50$, and bags of cookies cost $$2.00$, and sales equaled $$31.00$ in total. There were $6$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${7.5x+2y = 31}$ ${y = x+6}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+6}$ for $y$ in the first equation. ${7.5x + 2}{(x+6)}{= 31}$ Simplify and solve for $x$ $ 7.5x+2x + 12 = 31 $ $ 9.5x+12 = 31 $ $ 9.5x = 19 $ $ x = \dfrac{19}{9.5} $ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $ {y = x+6}$ to find $y$ ${y = }{(2)}{ + 6}$ ${y = 8}$ You can also plug ${x = 2}$ into $ {7.5x+2y = 31}$ and get the same answer for $y$ ${7.5}{(2)}{ + 2y = 31}$ ${y = 8}$ $2$ bags of candy and $8$ bags of cookies were sold.